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Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

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Abstract

With the two-scale expansion technique proposed by Yoshizawa, the turbulent fluctuating field is expanded around the isotropic field. At a low-order two-scale expansion, applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field, the Reynolds-average terms in the Reynolds stress transport equation, such as the convective term, the pressure-gradient-velocity correlation term and the dissipation term, are modeled. Two numerical examples: turbulent flow past a backward-facing step and the fully developed flow in a rotating channel, are presented for testing the efficiency of the proposed second-order model. For these two numerical examples, the proposed model performs as well as the Gibson-Launder (GL) model, giving better prediction than the standard k-ɛ model, especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.

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Authors and Affiliations

  1. Department of Thermal Science and Energy Engineering, University of Science and Technology of China, 230026, Hefei, China

    Xiao-Hong Wang, Zheng-Feng Liu & Xiao-Xia Lu

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  1. Xiao-Hong Wang
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  2. Zheng-Feng Liu
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  3. Xiao-Xia Lu
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Correspondence to Xiao-Hong Wang.

Additional information

The project was supported by the National Natural Science Foundation of China (10872192).

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Wang, XH., Liu, ZF. & Lu, XX. Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique. Acta Mech Sin 27, 649–659 (2011). https://doi.org/10.1007/s10409-011-0493-1

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  • DOI: https://doi.org/10.1007/s10409-011-0493-1

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